Is f(x)=x^a a Strictly Convex Function for a>1 on (0,\infty)?

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The function f(x)=x^a is indeed a strictly convex function for a>1 on the interval (0,∞). To determine this, the second derivative f''(x) is analyzed, which is found to be positive for all x in the specified domain when a>1. This positivity indicates that the graph of the function curves upwards, confirming its strict convexity. The discussion emphasizes the importance of the second derivative test in establishing convexity. Thus, f(x)=x^a is strictly convex for a>1 on (0,∞).
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Is it true that f(x)=x^a is always a strictly convex function for a>1 on (0,\infty)?
 
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Find the sign of f''(x).
 

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